Question

X = 2t y = t + 5, -2 ≤ t ≤ 3 Can you please graph this

Answer 1

Answer:

See attachment

Step-by-step explanation:

The given parametric equations are;

$x=2t$ and $y=t+5$, $-2\le t\le 3$.

We can graph this by plotting some few points within the given range or eliminate the parameter to identify the type of curve.

Plotting points;

When $t=-2$,

$x=2(-2)=4$ and $y=-2+5=3$

This gives the point (-4,3).

When $t=0$

$x=2(0)=0$ and $y=0+5=5$

This gives the point (0,5).

When $t=3$

$x=2(3)=6$ and $y=3+5=8$

This gives the point (6,8).

We plot these points and draw a straight line through them.

Eliminating the parameter.

$x=2t$

$y=t+5$

Make t the subject in the second equation;

$t=y-5$

Substitute into the first equation;

$x=2(y-5)$

This implies that;

$x=2y-10$

$y=\frac{1}{2}x+5$

This is an equation of a straight line with slope $\frac{1}{2}$ and y-intercept 5 on the interval

$-4\le x \le 6$

Answer 2

Answer:

The answer is in attachment

Step-by-step explanation:

First step finde a function t(x) ⇒ t=x/2;

Now we need to finde the limits of that function:

if t=-2 ⇒ x=-4 and t=3 ⇒ x=6. That means -4≤x≤6

Now replace on y(t) ⇒ y(x)= x/2+5, 4≤x≤6